Abstract

Addressing thousands of students entering unprepared to enroll in college freshman mathematics courses is a challenge two-year college mathematics faculty face every semester. The study addresses this challenge through a mixed methods sequential nested multi-case design to investigate what faculty need, beyond teacher knowledge, to teach mathematics effectively to students. The three-part study measured the mindset learning profile and content knowledge of a sample of mathematics faculty at a two-year college. The quantitative and qualitative data provided references to select four faculty typologies to interview and observe. Interviews reflected faculty perceptions of teaching and learning. Class observations captured images of faculty teaching. Narratives on lesson objectives measured faculty lesson objectivization. Open, expert, and meaning coding was employed to identify emerging themes in the analysis of data for the multi-case study. Analysis of both quantitative and qualitative data facilitated the integration of methods to investigate connections between faculty content knowledge, a mindset for learning, and teaching. A key finding from the study was that faculty with a knowledge of mathematics as a discipline, coupled with a growth mindset, engaged students in activities that develop meaningful and productive learning of mathematics. Data also reported a statistically significant relationship between content knowledge and lesson objectivization (Pearson’s r = 0.6148, p < 0.05). Other emerging themes included the following: two-year college mathematics faculty knowledge of content varies by domain; two-year college mathematics faculty demonstrated limited awareness of the guiding principles of learning sciences including but not limited to principles of effective learning in mathematics classrooms.